Question: Solve for $x$ and $y$ using elimination. ${-x-4y = -29}$ ${2x+3y = 33}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $2$ ${-2x-8y = -58}$ $2x+3y = 33$ Add the top and bottom equations together. $-5y = -25$ $\dfrac{-5y}{{-5}} = \dfrac{-25}{{-5}}$ ${y = 5}$ Now that you know ${y = 5}$ , plug it back into $\thinspace {-x-4y = -29}\thinspace$ to find $x$ ${-x - 4}{(5)}{= -29}$ $-x-20 = -29$ $-x-20{+20} = -29{+20}$ $-x = -9$ $\dfrac{-x}{{-1}} = \dfrac{-9}{{-1}}$ ${x = 9}$ You can also plug ${y = 5}$ into $\thinspace {2x+3y = 33}\thinspace$ and get the same answer for $x$ : ${2x + 3}{(5)}{= 33}$ ${x = 9}$